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Welcome to the Spotify Community!
You can listen to music in Spotify Premium offline, you can make sure that your account is premium by logging into spotify.com -> Account tab.
Also make sure that you are logged into the proper premium account in the iPad, if you are not sure, just log out and log back in again.
Under the Playlist tab in the iPad, you can click on an iPad playlist and hit on the black download icon beside the edit button and toggle on the offline mode.
If you are unable to see the download icon, please check your account, you might be signed in to the wrong account / your premium subscription might've expired.